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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 87120.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.bn1 | 87120t4 | \([0, 0, 0, -57499563, -167820468662]\) | \(15897679904620804/2475\) | \(3273096420633600\) | \([2]\) | \(3932160\) | \(2.8236\) | |
| 87120.bn2 | 87120t6 | \([0, 0, 0, -30492363, 63566853658]\) | \(1185450336504002/26043266205\) | \(68882522341166464296960\) | \([2]\) | \(7864320\) | \(3.1702\) | |
| 87120.bn3 | 87120t3 | \([0, 0, 0, -4138563, -1774758062]\) | \(5927735656804/2401490025\) | \(3175882183844361446400\) | \([2, 2]\) | \(3932160\) | \(2.8236\) | |
| 87120.bn4 | 87120t2 | \([0, 0, 0, -3594063, -2621673362]\) | \(15529488955216/6125625\) | \(2025228410267040000\) | \([2, 2]\) | \(1966080\) | \(2.4771\) | |
| 87120.bn5 | 87120t1 | \([0, 0, 0, -190938, -53675237]\) | \(-37256083456/38671875\) | \(-799095805818750000\) | \([2]\) | \(983040\) | \(2.1305\) | \(\Gamma_0(N)\)-optimal |
| 87120.bn6 | 87120t5 | \([0, 0, 0, 13503237, -12913790582]\) | \(102949393183198/86815346805\) | \(-229620202734149609564160\) | \([2]\) | \(7864320\) | \(3.1702\) |
Rank
sage: E.rank()
The elliptic curves in class 87120.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.bn do not have complex multiplication.Modular form 87120.2.a.bn
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
